ROOT   Reference Guide
ROOT::Math::VavilovAccurateQuantile Class Reference

Class describing the Vavilov quantile function.

The probability density function of the Vavilov distribution is given by:

$p(\lambda; \kappa, \beta^2) = \frac{1}{2 \pi i}\int_{c-i\infty}^{c+i\infty} \phi(s) e^{\lambda s} ds$

where $$\phi(s) = e^{C} e^{\psi(s)}$$ with $$C = \kappa (1+\beta^2 \gamma )$$ and

$\psi(s) = s \ln \kappa + (s+\beta^2 \kappa) \cdot \left ( \int \limits_{0}^{1} \frac{1 - e^{\frac{-st}{\kappa}}}{t} \, dt- \gamma \right ) - \kappa \, e^{\frac{-s}{\kappa}}$

. $$\gamma = 0.5772156649\dots$$ is Euler's constant.

The parameters are:

• 0: Norm: Normalization constant
• 1: x0: Location parameter
• 2: xi: Width parameter
• 3: kappa: Parameter $$\kappa$$ of the Vavilov distribution
• 4: beta2: Parameter $$\beta^2$$ of the Vavilov distribution

Benno List, June 2010

Definition at line 72 of file VavilovAccurateQuantile.h.

## Public Member Functions

VavilovAccurateQuantile ()
Default constructor. More...

VavilovAccurateQuantile (const double *p)
Constructor with parameter values. More...

~VavilovAccurateQuantile () override
Destructor. More...

IBaseFunctionOneDimClone () const override
Return a clone of the object. More...

double DoEval (double x) const override
Evaluate the function. More...

double DoEvalPar (double x, const double *p) const override
Evaluate the function, using parameters p. More...

unsigned int NPar () const override
Return the number of Parameters. More...

std::string ParameterName (unsigned int i) const override
Return the name of the i-th parameter (starting from zero) More...

const doubleParameters () const override
Access the parameter values. More...

void SetParameters (const double *p) override
Set the parameter values. More...

Public Member Functions inherited from ROOT::Math::IParametricFunctionOneDim
double operator() (const double *x, const double *p) const
multidim-like interface More...

double operator() (double x, const double *p) const
Evaluate function at a point x and for given parameters p. More...

Public Member Functions inherited from ROOT::Math::IBaseFunctionOneDim
IBaseFunctionOneDim ()

virtual ~IBaseFunctionOneDim ()
virtual destructor More...

virtual IBaseFunctionOneDimClone () const =0
Clone a function. More...

double operator() (const double *x) const
Evaluate the function at a point x[]. More...

double operator() (double x) const
Evaluate the function at a point x Use the a pure virtual private method DoEval which must be implemented by sub-classes. More...

Public Member Functions inherited from ROOT::Math::IBaseParam
virtual ~IBaseParam ()
Virtual Destructor (no operations) More...

virtual unsigned int NPar () const =0
Return the number of Parameters. More...

virtual std::string ParameterName (unsigned int i) const
Return the name of the i-th parameter (starting from zero) Overwrite if want to avoid the default name ("Par_0, Par_1, ...") More...

virtual const doubleParameters () const =0
Access the parameter values. More...

virtual void SetParameters (const double *p)=0
Set the parameter values. More...

## Private Attributes

double fP [5]

Public Types inherited from ROOT::Math::IParametricFunctionOneDim
typedef IBaseFunctionOneDim BaseFunc

Public Types inherited from ROOT::Math::IBaseFunctionOneDim
typedef IBaseFunctionOneDim BaseFunc

#include <Math/VavilovAccurateQuantile.h>

Inheritance diagram for ROOT::Math::VavilovAccurateQuantile:
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## ◆ VavilovAccurateQuantile() [1/2]

 ROOT::Math::VavilovAccurateQuantile::VavilovAccurateQuantile ( )

Default constructor.

Definition at line 40 of file VavilovAccurateQuantile.cxx.

## ◆ VavilovAccurateQuantile() [2/2]

 ROOT::Math::VavilovAccurateQuantile::VavilovAccurateQuantile ( const double * p )

Constructor with parameter values.

Parameters
 p vector of doubles containing the parameter values (Norm, x0, xi, kappa, beta2).

Definition at line 48 of file VavilovAccurateQuantile.cxx.

## ◆ ~VavilovAccurateQuantile()

 ROOT::Math::VavilovAccurateQuantile::~VavilovAccurateQuantile ( )
override

Destructor.

Definition at line 61 of file VavilovAccurateQuantile.cxx.

## ◆ Clone()

 IBaseFunctionOneDim * ROOT::Math::VavilovAccurateQuantile::Clone ( ) const
overridevirtual

Return a clone of the object.

Implements ROOT::Math::IBaseFunctionOneDim.

Definition at line 101 of file VavilovAccurateQuantile.cxx.

## ◆ DoEval()

 double ROOT::Math::VavilovAccurateQuantile::DoEval ( double x ) const
overridevirtual

Evaluate the function.

Parameters
 x The Quantile $$z$$ , $$0 \le z \le 1$$

Reimplemented from ROOT::Math::IParametricFunctionOneDim.

Definition at line 89 of file VavilovAccurateQuantile.cxx.

## ◆ DoEvalPar()

 double ROOT::Math::VavilovAccurateQuantile::DoEvalPar ( double x, const double * p ) const
overridevirtual

Evaluate the function, using parameters p.

Parameters
 x The Quantile $$z$$, $$0 \le z \le 1$$ p vector of doubles containing the parameter values (Norm, x0, xi, kappa, beta2).

Implements ROOT::Math::IParametricFunctionOneDim.

Definition at line 94 of file VavilovAccurateQuantile.cxx.

## ◆ NPar()

 unsigned int ROOT::Math::VavilovAccurateQuantile::NPar ( ) const
overridevirtual

Return the number of Parameters.

Implements ROOT::Math::IBaseParam.

Definition at line 74 of file VavilovAccurateQuantile.cxx.

## ◆ ParameterName()

 std::string ROOT::Math::VavilovAccurateQuantile::ParameterName ( unsigned int i ) const
overridevirtual

Return the name of the i-th parameter (starting from zero)

Reimplemented from ROOT::Math::IBaseParam.

Definition at line 78 of file VavilovAccurateQuantile.cxx.

## ◆ Parameters()

 const double * ROOT::Math::VavilovAccurateQuantile::Parameters ( ) const
overridevirtual

Access the parameter values.

Implements ROOT::Math::IBaseParam.

Definition at line 64 of file VavilovAccurateQuantile.cxx.

## ◆ SetParameters()

 void ROOT::Math::VavilovAccurateQuantile::SetParameters ( const double * p )
overridevirtual

Set the parameter values.

Parameters
 p vector of doubles containing the parameter values (Norm, x0, xi, kappa, beta2).

Implements ROOT::Math::IBaseParam.

Definition at line 68 of file VavilovAccurateQuantile.cxx.

## ◆ fP

 double ROOT::Math::VavilovAccurateQuantile::fP[5]
private

Definition at line 134 of file VavilovAccurateQuantile.h.

Libraries for ROOT::Math::VavilovAccurateQuantile:
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The documentation for this class was generated from the following files: